Simplify the following expression: $y = \dfrac{81q^2 + 90q}{18q^2 - 18q}$ You can assume $q \neq 0$.
Explanation: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $81q^2 + 90q = (3\cdot3\cdot3\cdot3 \cdot q \cdot q) + (2\cdot3\cdot3\cdot5 \cdot q)$ The denominator can be factored: $18q^2 - 18q = (2\cdot3\cdot3 \cdot q \cdot q) - (2\cdot3\cdot3 \cdot q)$ The greatest common factor of all the terms is $9q$ Factoring out $9q$ gives us: $y = \dfrac{(9q)(9q + 10)}{(9q)(2q - 2)}$ Dividing both the numerator and denominator by $9q$ gives: $y = \dfrac{9q + 10}{2q - 2}$